Question

Suppose we have a random sample of size 50 from a N(μ,σ2) PDF. We wish to test H0: μ=10 versus H1: μ=10. The sample moments are x ̄ = 13.4508 and s2 = 65.8016. (a) Find the critical region C and test the null hypothesis at the 5% level. What is your decision? (b) What is the p-value for your decision? (c) What is a 95% confidence interval for μ?

Answer #1

a) At alpha = 0.05, the critical value are t^{*} = +/-
2.010

Reject H_{0}, if t < -2.010 or, t > 2.010

The test statistic t = ()/(s/)

= (13.4508 - 10)/sqrt(65.8016/50)

= 3.008

Since the test statistic value is greater than the positive critical value (3.008 > 2.010), so we should reject the null hypothesis.

b) p-value = 2 * P(T > 3.008)

= 2 * (1 - P(T < 3.008))

= 2 * (1 - 0.9979)

= 0.0042

C) The 95% confidence interval for is

+/-
t^{*} *

= 13.4508 +/- 2.010 * sqrt(65.8016/50)

= 13.4508 +/- 2.3058

= 11.1450, 15.7566

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